The bus had just left a terminal near the Cantonment Railway Station when the bomb went off, witnesses and police officials said.
The incident occurred at a spot located less than a kilometre from Army House, the army chief's official residence when he visits Karachi.
TV news channels reported army chief Gen Ashfaq Parvez Kayani was in Karachi and had stayed at Army House last night.
Officials at Jinnah Hospital said they had received six bodies, including one which was in pieces, and 48 injured people. Eight of the wounded were in a serious condition.
Women and children were among the injured, they said.
Witnesses said they had seen body parts lying at the site.
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One man told reporters a young boy was torn in two by the explosion.
Several police officials claimed soon after the incident that the blast was caused by the CNG cylinders of the bus.
However, the cleaner of the bus told the media that the vehicle ran on diesel and had no CNG cylinders.
Police officials later acknowledged the incident was an act of terrorism and that a bomb had been planted in the bus.
The explosion hit several nearby shops, buildings, motorcycles and cars. A fire erupted in the bus, which was reduced to a heap of mangled and blackened metal.
Footage on television showed the bus on fire as a thick column of smoke rose into the sky.
No group claimed responsibility for the blast.
Security forces cordoned off area soon after the explosion.